Proof that SPIAs Still Make Sense

Today’s near-retirees face not only the usual risks associated with market volatility and longevity but also a lower average savings rate than previous generations and the reduced availability of traditional pensions. To ensure that they can sustain an acceptable standard of living in retirement and not run short of funds, they need new solutions.

One option is to add a source of income that they cannot outlive. In their landmark 2001 article in The Journal of Financial Planning (“Making Retirement Income Last a Lifetime”) John Ameriks, Bob Veres and Mark Warshawsky found that adding a life-contingent income annuity to a retirement portfolio reduces the rate that the portfolio will “fail” or go to zero.[1]

We ask if the benefits of lifetime income annuities persist today, when low interest rates have made annuity payout rates significantly lower than in 2001. Using annuity price quotes from CANNEX,[2] we measure the effects of annuitizing between zero and 30% of a retirement portfolio. We create a conceptual “retirement income frontier” that traces the trade-off between the sustainability of retirement income and expected financial legacy, using a framework established by Moshe Milevsky of Toronto’s York University.[3]

We’ll show that the 2001 results are in fact still valid: When a client buys an annuity with part of her savings, the sustainability of her income improves. While this improvement comes at a cost to her financial legacy, that cost can be overcome if she rebalances the rest of her portfolio to match her overall risk profile (i.e, with a shift toward equities).   

These results are produced for three reasons: the annuity income stream can’t be outlived; the pooling of longevity risk through the annuity enhances the retiree’s income (via “mortality credits”); and the retiree offsets the conservative effect of the annuity by taking more risk with the balance of her savings. The results hold true whether she’s a conservative, balanced or aggressive investor.

“Annuitizing a portfolio:” What and how?

First, let’s review what is meant by “annuitizing” (part of) a portfolio. In this article, we mean using a portion of retirement savings to purchase a single premium income annuity, or SPIA. While the SPIA is often overlooked in retirement income planning, it can provide a tremendous boost to the overall sustainability of a client’s retirement: For a one-time premium, the SPIA provides a lifetime of income. (Thus it functions like a workplace defined benefit pension.)

Despite the benefits it can offer, the SPIA is frequently shunned by clients and advisors alike. Why? The purchase decision is irreversible and thus the asset, although it produces income, is illiquid. This point of view, however, overlooks both the mortality credits that retirees acquire from pooling their assets, which provide a greater yield than products with similar levels of guarantee; and the lifetime nature of the SPIA income, which provides a hedge against an unknown and potentially longer-than-expected lifetime.

Ultimately, while a reliable source of retirement income may be replicated with investments in fixed income products, a SPIA provides a higher income than  other non-pooled, non-life-contingent assets or products do. Given the SPIA’s relative advantages, the low take-up of lifetime income annuities by retirees is known as the “annuity puzzle”– a riddle that academics and practitioners have pondered for decades. 

Portfolio sustainability: Do SPIAs still help?

In this article, we will explore the impact of adding a SPIA on our client’s Retirement Sustainability Quotient (on one hand) and her Expected Financial Legacy (on the other). Our conceptual retirement income frontier will trace out the trade-off between these competing outcomes—increased sustainability or increased financial legacy.

We assume that the client has her financial assets consolidated in either a managed account (a portfolio of stocks, bond, ETFs, mutual funds or any combination thereof) or some combination of managed account and a SPIA, in which the annuitized portion provides a pension-like lifetime income starting at retirement. We further assume that our client understands what her inflation-adjusted (assuming 2% inflation) future income needs will be and that she buys a cost of living-adjusted SPIA. In our analysis, the client coordinates withdrawals from her managed account with her annuity payment to match her desired spending amount.

We define retirement income sustainability as a function of first, the fraction of income annuitized and secondly, the “lifetime ruin probability” of the managed account.  The lifetime ruin probability, in turn, is the probability that the investment portfolio will be fully depleted while the retiree is living.

Mathematically, the Retirement Sustainability Quotient (RSQ) takes the following form:

RSQ = (1 – p) (1- fSPIA) + fSPIA = 1 – p (1 – fSPIA)

where p represents the ruin probability and fSPIA represents the ratio of the annuitized income to the client’s desired income. 

In the above equation, we measure retirement sustainability as the weighted average of the success probabilities (“success” defined as the cases in which the retirement income portfolio supports the desired withdrawals during the client’s lifetime). The annuity, by its very nature, has a ruin probability of zero (assuming no default risk of the insurance company); while the investment account has a “non-zero” ruin probability.[4]

As always in finance, there is an economic trade-off. If an annuity has no death benefit or refund feature, the added retirement sustainability it produces can come at the cost of a smaller “Expected Financial Legacy,” which is the wealth that the client will be able to leave to heirs.

We define Expected Financial Legacy (EFL) more formally as the expected value of the funds left over upon the retiree’s death, measured in today’s dollars. Technically, we calculate our client’s EFL by aggregating the present value of the probability-of-death-weighted account balances over time.*

Together, the two concepts of Retirement Sustainability and Financial Legacy form a frontier that helps us to better understand and model the trade-off between income sustainability and financial legacy introduced by the inclusion of life annuities.

Modelling legacy and sustainability along the Retirement Income Frontier

Now, on to our model. In our case study, given the illiquidity of the SPIA, and the irreversibility of the SPIA purchasing decision, we limit the allocation to SPIAs to 30% of our client’s initial wealth. With the remaining (non-annuitized) portfolio, we consider three kinds of asset allocation models: conservative, balanced, and aggressive.

We also consider two approaches:

First Approach: SPIA + No Change to Asset Allocation (“SPIA + No Change”)

In approach one, we assume our client maintains their asset allocation (whether conservative, balanced or aggressive) even after purchasing the annuity. That is, we do not adjust the allocation of the managed assets in response to the annuity purchase. 

Second Approach: SPIA + Modified Asset Allocation (“SPIA + Modified Portfolio”)

In our second approach, we proportionally adjust asset allocations within the client’s managed account, taking the allocation to the SPIA into account. The entire retirement portfolio then conforms to the original risk profile of our retiree (conservative, balanced or aggressive). That is, we change the asset allocation of our client’s investments once the client has purchased an annuity, viewing the annuity purchase as a bond-like allocation on the balance sheet.

In our analysis, we use a stochastic modelling approach. It incorporates two separate sources of uncertainty (namely, market returns and remaining lifetime) to explore how adding a single premium income annuity to a range of “traditional” investment portfolios affects both retirement income sustainability and financial legacy. (A similar analysis could be carried out with other types of income annuities, such as deferred income annuities, or even variable or fixed indexed annuities.)

While the Retirement Sustainability and Financial Legacy calculations can be carried out using Monte Carlo simulations, we chose to use the numerical and analytic methods that are available in QWeMA NumeRIcs®, a set of analytic tools which equip financial specialists to explore and solve questions in retirement income planning.[5]

From a technical point of view, for our analysis, market dynamics are stochastically modelled and we assume that asset returns are normally distributed so that asset prices follow a lognormal distribution. Finally, in modelling our client’s remaining lifetime, we use the Gompertz-Makeham Mortality model calibrated to RP2000 actuarial tables for calculating retiree life expectancy that are readily available from the Society of Actuaries.[6]

In our case study, the client is a 65-year old healthy female retiring immediately. She desires to spend 5% of her initial wealth annually, adjusted in subsequent years for inflation, which we assume is 2%. We consider three asset allocation models to perform our analysis, namely:

• Conservative portfolio: 30% equity and 70% fixed income
• Balanced portfolio: 60% equity and 40% fixed income
• Aggressive portfolio: 70% equity and 30% fixed income 

All calculations are performed on an initial wealth value of $1 which allows us to scale the client’s legacy value by her initial wealth.

Our model’s capital market parameters are based on J.P. Morgan Asset Management’s 2016 Long Term Capital Market Assumptions.[7] We chose U.S. Large Cap equity returns and U.S. investment-grade corporate bonds for the equity and fixed income returns, respectively. We assumed the long-term borrowing cost was 2.5%.